If we look at all periodic scales epimorphic with respect to a given val, a certain number will achieve the maximal possible number of consonant dyads with respect to a given consonance set. In the 5-limit, that set will be the 5-limit diamond, {6/5, 5/4, 4/3, 3/2, 8/5, 5/3}. In case of a tie, the tie can sometimes be broken by means of larger chords (triads, tetrads etc.) Connectivity of the graph of the scale is another way of rating harmonic content; algebraic connectivity is especially useful for this because it can take non-integer values and is easy to compute. Below we list a few examples.

5-limit

Five notes

semilim2
semilim3

Six notes, 6b val

dwarf6_5
cluster6e
x-wing1
x-wing2

Seven notes

zarlino
mavchrome6

Eight notes

semimaj1
semimaj2

Nine notes

mavdie1

Ten notes

blackchrome1
blackchrome2

7 odd limit

Seven notes

maxsev1
maxsev2

Seven limit marvel

Seven notes

Gypsy scale

Eleven limit marvel

Seven notes

marvel11max7a
marvel11max7b